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A disc of mass 500 g and radius 10 cm ca...

A disc of mass 500 g and radius 10 cm can freely rotate about a fixed axis as shown in figure. light and inextensible string is wound several turns around it and 100 g body is suspended at its free end. Find the acceleration of this mass. [Given: The string makes the disc to rotate and does not slip over it. g = 10 m `s^(-2)`.

Text Solution

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Let the mass of the disc be `m_(1)` and its radius R. The mass of the suspended body is `m_(2)`.
`m_(1)` = 500 g = `500×10^(−3)` kg =0.5 kg
`m_(2)` = 100 g = `100×10^(−3)` kg = 0.1 kg
As the light inextensible string is wound around the disc several times it makes the disc rotate without slipping over it. The translational acceleration of m2 and tangential acceleration of m1 will be the same. Let us draw the free body diagram (FBD) of `m_(1)` and `m_(2)` separately.
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